Every Monday for the past 7 weeks I’ve been attending a teaching credential class where I’m learning how to teach elementary students math. The class is focused on teaching students math through problem solving instead of introducing the algorithms first. This allows students to come up with inventive ways to solve a problem and find the answer. It’s a very interesting strategy that I’m trying to incorporate into my daily teaching, but sometimes I find it difficult since it’s not the way I learned math.

However, I’m learning some alternative ways to solve everyday addition and subtraction problems; new algorithms and methods that I never realized before. One of these is the subtraction algorithm called “borrow and pay back.” It’s the way many European and Spanish speaking countries solve their subtraction problems, and is similar to our borrow and regroup method of subtraction. The basis for how we learned math is ingrained in our behaviors, and this difference in a simple algorithm may be one cause of our problem with debt.

Before the 1930’s, the United States also solved subtraction problems using the borrow and pay back method and this was the method that was taught in school. It was changed due to a study that made students catch on to subtraction quicker. However, if you’ll note the names of both methods, there is a subtle difference that reflects our changing psychology of that era: borrow, borrow, borrow (also called the decomposition method). Below is a comparison of the two subtraction algorithms. They are quite similar, except in the borrow and pay back method, the numbers retain their place value. In our current borrow and regroup method, the numbers are isolated. Many students struggle with subtracting across zeros because of this.

Comparing Subtraction Algorithms

Looking at the borrow and pay back method (also called the equal additions method or Austrian method), you may have been confused as I was. But once it is explained, it makes much more sense. The algorithm is basically “borrowing” a ten from one place value, and “paying it back” in the other number in the place value next to it. Our current algorithm we use today borrows and regroups. There isn’t any paying back going on. Does this sound familiar?

So was this change in a subtraction algorithm also a change in the way we viewed money and credit? After doing a little more research I found some information on the study that changed the way we subtract, but not a clear understanding of why it caught on so quickly. The Brownell study in 1937 found that students using the “crutch”, or current subtraction algorithm that uses the decomposition method with crossing out the numbers going across, were able to solve subtraction problems quicker and more accurately than not using the crutch. The study only focused on the decomposition algorithm.  However, once the students learned how to complete the algorithm, they were no more proficient than students learning the traditional way. Basically students could learn how to solve a subtraction problem quicker, but they didn’t necessarily understand why they were borrowing  or regrouping the numbers.

It’s interesting that this new algorithm became popular around the same time as the Great Depression. Could the adults in charge of the Brownell study have been thinking differently about math, numbers, and money due to the financial stress and pressure of that decade? Why did the Brownell study only focus on the decomposition algorithm when using the “crutch”? And Why did it catch on so quickly? Many educators at the time disputed the study and many today feel the borrow and pay back method is much more efficient. Yet, textbooks today have continued to teach subtraction using the decomposition method with the “crutch.”

In my personal opinion, I think there was definitely a change in the way people viewed money and borrowing and this allowed the decomposition algorithm to catch on so quickly. The idea of a “crutch” or trick to solve the problems faster also helped speed up its popularity.

What are your thoughts? Did you learn subtraction through the borrow and pay back method or through the decomposition method? Do you think I might be on to something about the changing views of money, credit, debt, and borrowing? Or am I stretching this a bit?

Tuesday Tips - Will become a weekly standard

I love alliteration, what can I say. Monday’s are always hectic for me and I often can’t sit down to write an eloquent post, so I’ve decided to make Tuesdays a post about something frugal and environmentally friendly. As this is my first “Tuesday Tip” I’ll make a point to keep my tips organized into two categories: Frugal ways to save money and how the tip ties in with the environment. So here goes:

Tip #1 : Use your own reusable containers for water and food.

Frugal ways using your own containers saves you money:

• Carrying around a water bottle allows you to fill up your canister where ever you go, and it’s free (minus the cost of the bottle). Most places have drinking fountains or water spigets, and most restaurants serve water for free. If you aren’t one to fill up on “tap” water, you can fill your bottle before leaving home.
• Bringing your lunch to work in reusable containers saves you money. Not only do you save money bringing your own food, you save money on the zip lock bags you no longer have to purchase.
• Discounts for bringing your own canister. Some places give small discounts for bringing in your own cup. For instance, Starbucks offers a 10 cent off discount for bringing in your own cup.

Using your own container is better for the environment:

• Less trash to throw away after lunch. If you bring your own lunch to work in a reusable container, you won’t have to throw away the “wrapper” when you’re finished. Just take it home and rinse/wash it out or wipe it out (depending on its contents).
• No more paper or plastic cups to throw away (and less for the companies to produce in theory). Again, less trash is produced if you bring your own reusable cup.

Since I’m trying to keep my tips short and sweet (that’s the whole point of them), I’d love to hear feedback on how or if you use this tip.

Cougar Flats Tent. A nice two-room tent, my husband can actually stand up in it and he's over 6 ft tall.

With Spring Break upon us, or for some their children, the thought of going away has been swimming around in my mind as of late. Since this month has not been inexpensive based on my calculations, my best option (meaning least expensive) is either camping or a day / weekend trip to a nearby city. I’m lucky to live on the coast and in an area that has a temperate climate all year long, so my options are copious. Ideal camping destinations are within an hour or three at the most, and gorgeous day trips involving either travel by train or car are within the same amount of time; from San Diego to San Luis Obispo, or Ojai to the Sequioas, the price for living in Southern California is sometimes negated by the glorious destinations within a 200 mile radius.

I’ve decided to break down my options by type, instead of price. Though the price range is similar, the experiences are not. First let me explore camping, something I love to do. Over the years, my husband and I have acquired enough camping equipment to make camping very comfortable (I also won’t be factoring this into the overall cost since it’s been compounding over the years). We are still “roughing” it in a tent, but our tent is larger (in comparison) than a studio apartment in New York. Below are some camping benefits:

• Beautiful scenery. Again, I’ve got weather on my side and a choice of desert, valley, mountain, or coast locations to choose from. I like to use ReserveAmerica.com to reserve campground spots. They show you an actual map of the campground sites and, if the campground allows, you can select your exact spot. This has come in handy when camping at both unknown areas and familiar ones. For instance, we like to camp at Wheeler Gorge. A creek runs through the entire campground and some sites are closer to the water than others. Their map allows me to reserve my favorite camp site, number 41, exactly where the creek bends. (I realize I just gave away my favorite site!) There is a small fee attached to booking through this site, but it makes up for it in convenience. Most camp sites range between $10 a night to $20 a night.
• Peace and quiet. Most campgrounds have a “lights out” policy and by 10 pm campers are required to whisper, or at least not whoop it up. For the most part, this is enforced. My husband and I have only had two problems (one really wasn’t a problem, just a very loud couple – if you get my drift.) One of the worst problems we ever encountered was a small campground that did not have a ranger on site, too many people in one campsite partying all night is not the ideal camping experience. We now make a point to camp at places that have a site manager or ranger.
• A camp fire. Who doesn’t love campfires? Roasting marshmallows over the fire, sitting so close you have to jump back to make sure an ember doesn’t land on you. Another benefit to booking online is making sure your campsite allows campfires and comes with a fire ring. Living in SoCal has made me very fire conscious, and we have learned the hard way that not all campgrounds allow camp fires. (P.S. The thought of marshmallows is much better than the real thing. After eating one or two, I’m done!)
• Hiking. Many of the campgrounds I stay at are within national parks. Most national parks have ranger stations where you can pick up a map that details the hiking trails. My husband, who is a good sport but not an extreme hiker, likes to choose the easier hikes that are under a 2 hour time span.

Making our camping comfortable has been a learning experience. We’ve now gotten savvy to a camping checklist and make sure we run through it before leaving. Organizing our camping gear in large, clear rubbermaid bins has also helped. Some things we take making camping comfy are a tackle box full of cooking utensils and spices, a blow up air mattress, an air compressor to blow up the bed, two camping stoves, an ice chest, camping dinner ware and cookware that stays in the garage all year long (we wash them before and after our trip), flashlights, lanterns, matches, and a portable heater in case of cooler nights. (And lots of propane!) Total cost of camping, including the cost of the site and groceries is usually around $200 for a three day trip. This price could be reduced based on the type of groceries purchased, but my husband loves grilling up filets while camping.

Our second option is a day trip to a nearby city. We have a couple of choices for traveling to a place such as Santa Barbara, San Diego, or San Luis Obispo. We can either drive, hauling our bikes on our bike rack, or take an Amtrak train. A couple of years ago we opted for the train to Santa Barbara. It was my first experience on a train and I loved it! Not only could we place our bikes in their luggage car, but the seats were really big and comfortable and you could get up and walk around to the diner car. The travel time wasn’t much more than if we had driven. Below I’ve outlined some benefits of a day trip (either by car or by train):

• Explore a quaint ocean city by bike. I’ve mentioned how much I love my bike before, but one thing I’ve noticed about cities such as Santa Barbara and San Diego is how bike-friendly they are. Bike lanes are clearly painted on most of their streets. Biking also lets you see each individual store and restaurant much clearer than driving past them.
• Bar hop. Yes, I know I shouldn’t be biking and drinking. However, I do feel it’s safer than drinking and driving. At least the only person I can injure is myself.
• Check out the residential neighborhoods. Exploring coast line cities is always fun, and checking out their residential architecture is something I like to to, whether on a bicycle or in a car.

There are definite benefits to both driving and taking the train. Train rides are generally a little more expensive. For instance, our trip to Santa Barbara cost us $67 for two people round trip. Driving, we probably would have spent about $30. When I factor in shopping and dining in a nearby city the cost ends up being very close to camping, hovering around $150 – $200.

What trips are you planning this spring or summer? Are you finding ways to save money? Are you staying close to home?

Finding low cost options for traveling to a funeral.

Man, if you look at my last post and this one, you’re surely thinking I’m obsessed with death. Not so, I say. However, death is a certainty no one can escape. And with death, comes funeral services. And with funeral services, comes family members scrambling to make it to the burial service. With last minute travel arrangements underway, getting the best deal is imperative. This past week my husband’s grandfather passed away, it was his last remaining grandparent. (My last remaining grandparent died over 10 years ago and I attended his funeral.) He made the decision that he would travel to Nebraska for the services, and because it was financially too expensive for me to accompany him with missing work plus the additional cost of a flight, we decided I would stay home. I honestly only met his grandfather once 11 years ago, so I was okay with this arrangement. I’m sure you are now realizing why I’ve been focusing on death this week!

Since death is imminent, yet elusive, meaning you can’t pinpoint the exact date of death, booking travel arrangements last minute can become costly. I’m the financial accountant around here, so I’m usually the one in charge of searching for the most economical airfare. We had less than 4 days from the time of notice to the day of the funeral to book the flight. I immediately began searching multiple travel websites. Travelocity.com is always the first website I scope out since they were one of the first online travel sites, but one I’ve recently started using that searches multiple sites at once is Kayak.com. Not only does Kayak search their own database for the lowest fares, it gives you the option of searching an additional 5 sites (this helps me remember all of my options): Priceline, Hotwire, Travelocity, Expedia, and Airfare.com. Smaller browser windows pop up on your desktop so that you can literally compare their rates side by side. This is by far their best advantage compared to other online travel sites.

After glancing at all of the different sites plus the flights on Kayak, I found the best price and shortest flight time (very important since my husband hates traveling!) on Priceline.com. For under $600 we were able to book a round trip flight that would allow my husband to arrive the day before the funeral. Unfortunately, he had to say an additional day longer than he would have liked or pay twice the price for the flight. Funny how returning on a Saturday is half as much as returning on a Friday. Some tips if you’re ever in need of last minute flight arrangements:

• Search multiple sites, or use Kayak to do this for you, for the best price.
• Be a little flexible if you can. For instance, my husband made the choice to stay one day longer even though he really wanted to return a day earlier. Luckily he was staying with relatives, so the cost of a hotel didn’t have to be factored in here.
• If you know you have to book a flight for a funeral, do it as soon as you know the date of the funeral, don’t wait! My mother-in-law waited one additional day to book her flight and it cost her quite a bit more money.

Death is an uncomfortable topic for some, but it is an event that happens once in everyone’s life. Being able to attend a funeral of a loved one gives people closure, and being able to do that without going into debt relieves some of that stress.

On a side note, I didn’t contact the airlines directly and ask for a bereavement fare because in my experience, the online rates are usually less expensive.

Have you had to make last minute flight arrangements due to a death or emergency? What did you do to minimize the flight cost? Have you used Kayak for booking your travel needs?

Cut up those credit cards?

One of my goals for this year, that I have partly accomplished, is raising my credit score. I need to get my score above 740, at minimum, so that when I apply for a mortgage loan, I’ll be able to get the best rate. I still need to raise my score about 40 points (this is an average as all 3 credit bureaus are reporting slightly different scores). One thing I’ve learned about improving my credit score, is keeping my debt to credit ratio low. Since I’ve paid off all of my credit cards, I’m looking pretty good here. However, another factor that affects a credit score is how much total credit banks are willing to loan you. Since I’ve been on a mission to improve my poor credit history, I haven’t had much credit extended to me these past few years leaving me with very low credit limits.

So, here is my dilemma: I have two credit cards with low credit limits that are charging me monthly fees and/or annual fees (totaling approx. $155 for the year) . I don’t use these cards at all anymore. However, there is a catch with these two cards: they were originally a way to pay off old collection debt. These cards were offered to me about 6 years ago to pay off two other credit cards that had gone into collections. Once I paid the old debt off in full, they extended a limited amount of credit to me. I’m now thinking of canceling these two credit cards now that they are paid in full, but then my overall total available credit limit will be reduced by almost $1,000. How will this affect my credit score? Will it ding my score by a few points? Since I’m hoping to apply for a mortgage loan with in the next year or so, I’m trying very hard to keep the activity on my credit report to a minimum.

After doing some research, canceling my two credit cards would probably affect my credit score a little bit. By how much, I don’t know exactly. I have two options; A.) I cancel these cards and save $155 annually, with the potential of losing a few points off my credit score, or B.) I keep these cards until I am able to purchase a home.  That could be up to 18 – 24 months meaning I would have to spend up to $310 on fees, but I’d be saving my credit score.

For now, I think I will keep the cards. If purchasing a house becomes ever more elusive and my time frame extends to more than 24 months, I might just go ahead and cancel these two cards. I do know that when I obtain that mortgage loan, these two cards are getting the ax!

What do you think? Would canceling these cards now be beneficial? Am I making the right choice by keeping these cards a little longer?

I'm burning my candle at both ends this week.

I’m posting this mid-week because 1.) I didn’t post any round-ups this past weekend, and 2.) I’m really behind on some projects…crap!  Some terrific articles have been written on various Yakezie member sites that I’d like to share, instead of banging out an article of my own. Enjoy!

• Sweating the Big Stuff and How to Raise Your Credit Limit (This also touches upon hard inquiries and soft inquiries)
• Young and Thrify and What’s Your Latte Factor? Of course I had to read this one! I love my Starbucks. However, it does make me think about spending my $2.50 daily. It sure adds up!
• Ultimate Money Blog is running a whole series on state economies. I love statistics! This one is about Alaska. So who wants to live near Sarah Palin?
• Rainy Day Saver changed the look of her blog too. I like it! Check it out. (P.S. I’m still working on mine )
• My Money Minute and Wine on a Budget. I personally am more of a beer drinker, but who doesn’t love wine? Okay, me. But most people like it.
• Monevator plays devil’s advocate on Wasting Money on Memories. Yet, the conclusion is well done.

Since I’m burning the candle at both ends this week (to use a figure of speech), I will make a point to post something meaty in the next day or so. Please hang in there,  I’m just juggling too many jobs right now. (That’s a good thing, though. Right?  )

Ventura County at dusk

I love exploring city statistics, comparing them with the city I live in, and making comparisons to cities I contemplate moving to. One site I always go back to is BestPlaces.net. I can quickly use their city compare link and glance through their copious amounts of data. (The one draw back to using this site is much of their data is a few years old. I’m hoping that when the 2010 census is published, they will update their statistics.) Another feature I find helpful is personal quotes and opinions about cities that people leave on their site. This helps narrow down the positives and negatives of an unknown city.

I use this site when considering my options for moving. For instance, I’m currently thinking of moving to a neighboring county, Ventura. It’s only a 30 minute drive away from where I live in Los Angeles County. But their population is 1/10 the size. According to Google, Los Angeles County is busting at the seams at almost 10,000,000 people – Whoa! Ventura County’s population, just to the north west, is under a cool million.  Ventura County is almost half the size, but even factoring this in, the population density is 1/6th of that of LA County (according to Wikipedia). What a difference! Less density means:

• Less traffic! A huge problem with LA county.
• Better, smoother roads due to fewer cars. I’m really tired of the pot holes chewing up my car.
• Less people! I love our city’s diversity, but I feel a little like a sardine lately. Too many people in such a small area.
• Better bicycle infrastructure. Ventura county is more bike-friendly with bike lanes painted on most of their roads.
• Less graffiti. Because we have so many people, there’s more chance of hoodlums messing up the city. Lately, many of them have been having a heyday with spray paint!

When comparing counties, I’m also looking for a little break in the cost of living. According to BestPlaces.net, I will be saving money on most of my expenses. Below is a graph directly from their website:

City Cost of Living Comparison

I’m not claiming Ventura County is cheap in any sense of the word. But it is cheaper than where I live.

Another factor to consider is their employment, or unemployment rate, and future expected growth. Los Angeles, and California in general, is pushing an unemployment rate of 13%. Ventura, however, is slightly lower than that. Since I will also have to search for a new teaching job, or something temporary for a while, this may bring me more prospects. You’ll also notice from this data below that most people in Ventura make more money than those in LA county, promising at least!

Cost of Living

Because this data is slightly outdated, I know that the sales tax has increased about 1%, but it has all over California. Ventura County’s sales tax is still 1% or more less than LA’s. Again, another reason for me to think seriously about moving.

On a side note, Ultimate Money Blog is doing something similar, but comparing all 50 states. I find this data fascinating. If any one is thinking of moving out of state, this might be a good window into what other states have to offer. If you use her descriptions along with BestPlaces.net city comparisons, you might find a city and state you would prefer to live in.

What city do you live in? Have you recently moved to a new city? What data did you use? Are you contemplating moving?

Our Honday Element "Ellie". It's what inspired up to go camping!

Today, my husband refinanced our Honda Element. I wasn’t too thrilled about the idea at first, because it meant having car payments for a longer period of time. But after doing the math, we realized we would be saving money.  Over all it means we will be paying a few months longer, but will be saving over $2,400!

Here is how it played out, you can be the judge and decide if it was a good move or not (I love feedback!)

• Our current auto loan APR was 9.98%. Not great, but when my husband first financed the vehicle, his credit was in the low 600’s, not very good.
• Our current auto payments with the 9.98% loan was $475 a month. We’ve owned the car almost 4 years, so this was a high payment for the length of time we’ve owned the car, and we still had 22 months to go. We owed $9,500 on the car.
• The new refinanced loan is now 7.25%, this is more than 2 percentage points less. Better credit score equals better APR.
• Our new payment will be only $319 for 33 months. This is the stinker part of the refinanced loan, the length of time. This adds almost a whole year onto the new loan. However, there isn’t a penalty for paying it off early. We can also save another half a percent on the loan if we set up auto-debits and we will definitely be doing this!
• I calculated my monthly savings: $156 saved per month. This equates to a savings of $3,432 over 22 months (the original length of the first loan). Since I’ll be paying about $1,000 more in interest, because the loan was extended, I deducted the $1,000 off the saved monthly amount. This leaves me with a total savings of $2,432.

Overall, I think this was a good move. I don’t like that we will be paying for the car longer. However, because there is no early payoff penalty, I might still be able to pay the car off in two years. If I don’t pay it off early, at least I know I’ll be able to stick the savings of $156 a month into savings. With a meager savings rate of 1.14% in two years I should be able to save:   $3,786.21 based on Bank Rate’s simple savings calculator and compound interest. (This is if every dime of my savings get deposited into my savings account!)

What are your thoughts? Was this a good move? Should we have stuck it out with the higher payment and APR, but shorter time period?

This photo reminds me of the journey towards financial freedom; lots of steps that are sometimes elusive.

I’m realizing that my goal to purchase a house with in the next year is still many months away. I started out with a 3-step plan: pay down debt, raise my credit score, save for a down payment. My first two goals are going swimmingly; I’ve paid off close to $8,000 in debt and am working towards paying off my line of credit and my car loan. I used a debt repayment calculator and found that at the rate I’m going, I should have both paid off in under two years. That’s great news, if I can pay it off before then, even better. I’ve also raised my credit score by over 100 points in a year. All there is for me to do is keep making my student loan payments, use my credit cards lightly, then pay them off in full every month. If I keep this strategy up, I should see a 740 score this year.

However, I’m struggling with the 3rd step of my plan: save a down payment. These last few months my income has waned. As a a temporary employee with a school district that is running out of funds, I’m seeing this as a long-term pattern. My husband’s business is doing okay, but he is only bringing in enough income to equate to one salary plus a part-time employee (who is a programmer). This means I have to develop a new plan for bringing in more income.

My plan is still in the fuzzy- vague-I’m not sure what I’m going to do yet stages, but at least I have a direction:

• Option A: Be a marketing genius and bring in more work for my husband, which would create a job for me. This plan is more long-term and the results wouldn’t be immediate. However, if I am successful, it would be my ideal option.
• Option B: Take on a part-time position with a local company or the Census Bureau. This would bring in extra cash for a few months while I develop a more long-term strategy, still allowing me to take teaching gigs.
• Option C: Stick it out with the current school district and hope their budget improves. This is a risky scenario, I don’t want to wait until the bitter end only to find out I was right all along.
• Option D: Go get a permanent position and switch professions. I’ve been teaching for almost 9 years, I haven’t had to work in a corporate office or go on a job interview in a very long time. I like my summers off and my three weeks of winter break. This option scares me!

As I switch gears and begin moving towards option A, I realize I need to be really organized and manage my time wisely. I can easily fall into a pattern of sleeping too late, or wasting time running errands when I ‘work’ for my husband. To optimize my time, I’ll begin focusing on tasks using my task manager in Outlook. This should keep me in line.

Have you had to change jobs lately? How do you manage your time when you’re at home? Which option would you choose if you were in my position? Do you use a program to help organize your tasks?